Control of uncertain nonholonomic mechanical systems using differential flatness

Abstract

Considers the problem of controlling uncertain nonholonomic mechanical systems which are differentially flat, that is, which admit a set of (flat) outputs with the property that there is a one to one correspondence between system trajectories and output curves. It is proposed that a simple and effective solution to this problem can be obtained by combining a trajectory generation algorithm for the flat outputs with an adaptive tracking scheme for a set of "reducing" outputs; these reducing outputs are a subset of the configuration coordinates and are easily obtained. This approach is shown to ensure accurate motion control despite considerable uncertainty regarding the system dynamic model, and to be generalizable to provide compensation for uncertainty in the kinematic model as well.